Table of contents

Contents Introduction § 1. Banach manifolds and their maps § 2. The degree of a Fredholm map § 3. Equivariant Fredholm maps § 4. Solubility of equations with Fredholm operators § 5. Some applications to existence theorems for differential equations § 6. Complete and local invertibility of proper maps § 7. Intersection indices References

CONTENTS Part I § 1. Introduction § 2. Prerequisites from ergodic theory § 3. Basic properties of the characteristic exponents of dynamical systems § 4. Properties of local stable manifolds Part II § 5. The entropy of smooth dynamical systems § 6. "Measurable foliations". Description of the π-partition § 7. Ergodicity of a diffeomorphism with non-zero exponents on a set of positive measure. The K-property § 8. The Bernoullian property § 9. Flows § 10. Geodesic flows on closed Riemannian manifolds without focal points References

Contents Introduction § 1. Sublinear operators § 2. Application of sublinear operators to the study of semigroups § 3. Superlinear point-set mappings References

Contents Introduction § 0. Definitions, notation, and basic facts § 1. The universal 1-form. Lagrangian manifolds § 2. Fields and 1-forms on Φ § 3. Poisson brackets § 4. Symmetries § 5. The structure of Hamiltonian systems with a given degree of symmetry § 6. Completely integrable systems § 7. The theorems of Darboux and Weinstein § 8. Invariant Hamilton-Jacobi theory § 9. Hamiltonians of mechanical type § 10. Mechanical systems. Examples Appendix I. Bifurcations Appendix II. A. V. Bocharov and A. M. Vinogradov, The Hamiltonian form of mechanics with friction, non-holonomic mechanics, invariant mechanics, the theory of refraction and impact References